The present invention relates to a method to predict the future data on the basis of the measured data which are continuous in time series.
Vertical cylindrical furnaces called cupolas, used to melt gray cast iron for casting, are known in the prior art. Each cupola has a bed of coke at the bottom. Unprocessed metals, coke and flux are thrown into a top of the cupola and melted in the presence of blowing air. The cupola is used to get the good molten metal out of a tap hole. The most important items to control in this process are temperatures, composition, gas content, and the chill of the molten metal. Materials to be thrown into the cupola and factors relative to the air blowing are especially important among the factors which effect the temperature and the composition of the molten metal.
In the cupola, since the added materials gradually move down to the molten metal zone at the bottom, it takes dozens of minutes before the changes brought by the added materials effect temperatures or the composition of the molten metal at the tap hole. This also happens when factors relative to the air blowing change: a time-lag (called dead time) occurs before the changes appear among temperatures and composition of the molten metal at the tap hole. FIG. 11 is a graph which shows the relation between the molten metal temperature and quantity of blown air. As FIG. 11 shows, although the quantity of the blown air increases at the point the dashed line a shows, there is a delay before the temperature of the molten metal rises.
Therefore, in order to get good molten metal regularly from the cupola, it is important to adjust the thrown materials as well as factors relative to the air blowing, while capturing the change of the temperature and composition of the molten metal as soon as possible. In other words, in order to eliminate the above-mentioned time-lag, it is necessary to take into account the dead time (which may be a few dozen minutes ), predict the temperature and composition of the molten metal, and adjust the materials to be thrown into the cupola and factors relative to the blowing air in accordance with the prediction.
There are several methods known that can be used to predict such continuously changing data as the above-mentioned molten metal temperature. One of them is a method to classify the transitions of the measured data values as some sort of pattern and predict values by referring to that pattern. Another value prediction method applies the method of least squares to the measured data. There is also a method that includes using multiple regression analysis with the time-lag taken into account, among other methods that use causal relation with the statistical analysis.
However, the above-mentioned classification, least squares, and multiple regression analysis methods are not perfect for predicting. For example, it is especially difficult to predict the value of a few minutes ahead. As a result, workers often control devices such as the above-mentioned cupola which need the predicted value, according to their experience and intuition. FIG. 12 shows the measured value 5 and the predicted value of the molten metal temperature in the cupola plotted on the same time axis by using the multiple regression analysis. As FIG. 12 shows, the predicted value can deviate from the measured value.
Wherefore, an object of the invention is to precisely determine a predicted value at a future point of time-series continuous data based on measuring points of the time-series continuous data and measured values at the measuring points.
To attain this and other objects, the invention provides a method of predicting time-series continuous data in which plural measuring points and measured values at the measuring points of the time-series continuous data are stored beforehand, and a predicted value of the data at one prediction point is determined via an interpolation formula based on the stored measuring points and measured values.
An interpolation formula as used herein means a curve which correctly passes along each of a series of values measured at corresponding measuring time points, which are used for preparing the interpolation formula, as described later. Known formulas include, for example, Newton""s interpolation formula and Lagrange""s interpolation formula.
Generally, in an interpolation formula, a value in a measuring period is interpolated by using known measuring points and measured values. In the present invention, the interpolation formula is prepared by using n (natural number) measuring points, known values at the measuring points, a prediction point, and an unknown value at the prediction point. In the interpolation formula, according to the concept of interpolation, the known measured value at the closest measuring point is interpolated from the closest measuring point in the measuring period. Therefore, the unknown value at the prediction point can be determined by counting backwards. As a result, an unknown value outside the known measuring period can be determined by using the interpolation formula.
According to the invention, the measuring points and the values corresponding to those points are first stored beforehand. As an illustration, FIG. 3 shows data measured in time series. In the graph, Q0 is a measured value at a measuring time or point t0, Q1 is a measured value at a measuring time or point t1, and so on for Q2/t2 and Q3/t3. When these four measuring points t0 to t3 and values Q0 to Q3 are stored, a prediction time point is represented by t4.
Next, the measurement point (among the measuring points prior the prediction point) which is closest to the prediction point is sampled. In FIG. 3, point t3 is the measuring point which is closest to the prediction point t4.
An interpolation formula is provided that can derive a value at a closest measuring point from the closest measuring point itself (that is, xe2x80x9cmeasured value=f(closest measuring point)xe2x80x9d, where the function is the interpolation formula). In FIG. 3, the measured value Q3 can be derived at the closest measuring point t3 in an interpolation formula f(t), that is, Q3=f(t3).
Next, as mentioned, the interpolation formula is prepared from past n measuring points before the closest measuring point, measured values at the measuring points, the prediction point, and the predicted value at the prediction point. In FIG. 3, n=2, which means specifically that two past measuring points t1 and t2 are used, and the measured values Q1 and Q2 at the measuring points t1 and t2 are used. If Lagrange""s interpolation formula is used, for example, Lagrange coefficients C1, C2 and C4 (corresponding to time points t1, t2, and t4, respectively) are obtained by differences among the points t1 to t4. Thus
f(t3)=C1Q1+C2Q2+C4Q4.
And, since f(t3)=Q3 (a known value),
Q3=C1Q1+C2Q2+C4Q4 and therefore
Q4 (unknown value)=(Q3xe2x88x92C1Q1xe2x88x92C2Q2)/C4.
According to the present invention, the degree n of the interpolation formula can be optimized.
In the invention, a control method can be realized by using the prediction methods. Specifically, in the control method, the predicted value (from the data entered from a control system) at the prediction point is determined by using one of the prediction methods, and the control system is controlled based on the determined predicted value. Examples of control systems include a power supply control system, an air conditioner control system, or a system to control a cupola or other furnace. As a function for realizing the execution of the prediction or control method in computer system, a program to be activated in the computer system may be provided.